Although this (very nice) paper is focussed on past climates, Fig. 8 shows a remarkable feature, the H1104 tephra appearing as a dislocated and deformed series of layers. The authors conclude that  the deformation may have arisen as a consequence of a large earthquake (such an event potentially being that recorded in 1260 CE). I agree with the interpretation that the deformation is seismic  in origin. Our research group in North island, New Zealand, based at University of Waikato in Hamilton, has been working on similar-looking deformation of lacustrine tephra layers in a series of ~20,000 year-old lakes in the Hamilton Basin. We have demonstrated using X-ray computed tomography (CT) imaging and laboratory work involving engineering geology, plus tephrostratigraphy etc, that the layers have been deformed and liquefied by seismicity. We have coined the term "tephra seismites" for the deformed layers (such as shown in Fig. 8. of Harning et al.).

I can recommend the authors consult a comprehensive paper we published last year: Kluger et al. 2023 Sedimentary Geology (copy attached to this comment), including supplementary information that includes CT scan images etc (available at https://doi.org/10.1016/j.sedgeo.2022.106327)

We also published two presentations about some of the work (presented at IAVCEI Congress, Rotorua, NZ, Jan-Feb 2023)  online at: 

https://www.researchgate.net/publication/369184266_Using_ground_penetrating_radar_and_Xray_computer_tomography_to_survey_and_characterise_distal_tephras_in_lake_sediments_Hamilton_lowlands_New_Zealand

https://www.researchgate.net/publication/369197768_Tephra_seismites_preserved_in_unconsolidated_organic_lake_sediments_in_the_Hamilton_lowlands_New_Zealand_indicate_paleoearthquake_activity_since_176_ka

See also our Tephra seismites Newsletter No. 3 (at https://tephra-seismites.com/updates/https://tephraseismites.files.wordpress.com/2023/06/tephra-seismites-newsletter-3.pdf - 26 June 2023 entry)

David Lowe

University of Waikato, Hamilton, NZ